As of October 26th 2019, it will not be possible to climb Uluru:
In line with the agreed process in the Uluru-Kata Tjuta National Park Management Plan 2010-2020 and the wishes of traditional owners, the climb to the top of Uluru will close on 26 October 2019.
I doubt you're going to find an "official" listing anywhere. Reading between the lines of the article, it sounds very much like this is still an active cemetery, meaning that there's points where it's open.
During my visit, I counted at least half a dozen signs warning visitors that trespassers would be prosecuted, even though the front gate was wide open ...
Please don't do this. Uluru is sacred to the Pitjantjatjara Anangu. You wouldn't like if if some foreigner came to your country and started climbing up your sacred monument.
Since there seems no other way to comment on the deletion of my answer:
I did read Craig's (very recent) answer but didn't think it came over as a definite "don't do it" kind of ...